In a trapezium ABCD, AB is parallel to CD and the diagonals
In a trapezium ABCD, AB is parallel to CD and the diagonals intersect each other at O. What is the ratio of OA to OC equal to?
- Ratio of OB to OD
- Ratio of BC to CD
- Ratio of AD to AB
- Ratio of AC to BD
Answer
The diagonals are transversals, so the following angles are equal:
∠BAO = ∠DCO and ∠ABD = ∠CDO. Thus by AA, the triangles ABO and CDO are similar.
Theorem: Given a trapezium ABCD with parallel sides AB and CD, let O be the intersection of the diagonals AC and BD. If the ratio r = AB/CD, then the diagonals are divided by this same ratio: AO/CO = BO/DO = r. Since the triangles ABO and CDO are similar, then these are ratios of corresponding sides.
The correct option is A.